A family of non-restricted $D=11$ geometric supersymmetries

Abstract

We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $\nu =\frac{3}{4}$. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decomposable spaces. These singular spaces are associated to a restricted $N=4$ geometric supersymmetry with $\nu =\frac{1}{2}$ in dimension six and a non-restricted $N=2$ geometric supersymmetry with $\nu =\frac{3}{4}$ in dimension nine.

26pp, v3: compared with the published version we clarified the content of Section 7 and corrected one of the interpretations

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